When dealing with quantum systems comprising particles or any degrees of freedom having discrete or continuous quantum states (such as an ensemble of spins, but also for example, quantum dots, photons, electromagnetic coherent states, harmonic oscillators and other such systems), at finite temperature, often thermal or systematic noise come in the way.
For example in spectroscopy based on nuclear magnetic resonance (NMR) this noise severely limits the usages of NMR for identifying and characterizing materials. Cooling techniques can then be used to reduce the noise, and therefore to improve the usefulness of the NMR technique.
NMR is a technique for studying nuclear spins in magnetic fields. NMR spectroscopy techniques (and similar techniques, e.g., quadrupole resonance) are extremely useful in identifying chemical materials (even identifying negligible amounts of them). There are numerous NMR applications in biology, medicine, chemistry, and physics, for instance identifying malfunctions of various body organs, identifying materials for police and army usages, monitoring brain activities, monitoring the purity of materials, and much more.
The signal to noise ratio is an important factor in NMR usages and techniques. The problem is that when the signal is not sufficiently clear or the noise is too strong, there would be difficulties in identifying the materials. There are several potential solutions that can improve the signal, but each of them has its problems. Note that in this pretext we refer to spin-half nuclei for which there is a simple one to one correspondence between cooling a spin, increasing its polarization bias, and reducing its entropy.
The first four potential solutions are:                1) Cooling the system (this cools the spin as well, therefore increases its polarization bias, therefore also increases the signal). Limitation: Usually it is irrelevant because it affects the results of the test by modifying the inspected molecules (e.g., solidifying the material), or by destroying the sample (e.g., killing the patient).        2) Increasing the magnetic field. Limitation: A much too expensive solution.        3) Increasing the sample, Limitation: It is usually impossible due to machine's limitations, or sample limitations. This is since one needs to increase the sample's size by a factor of M2 in order to improve the signal-to-noise ratio by a factor of M.        4) Collecting many results is a possible and most common solution. Limitation: In order to improve the signal-to-noise ratio by a factor of M, spectroscopy requires M2 repetitions. Therefore it becomes too time consuming in many cases (causing, for instance, high costs). It is even impractical in many other cases due to evolutions of the sample during the spectroscopy (e.g. changes in concentration of a material in some body organ, such as lungs). This is true especially because of the long recovery time between measurements. Furthermore, the repetition solution is not so useful if the noise considered is not a Gaussian noise.        
The next two potential solutions are ways for cooling the spins (increasing their polarization bias), without cooling the environment (the molecules). This can be called an “effective cooling” of the spins. Such cooling is as good as regular cooling of the system, because the cooled spins can be used for spectroscopy, as long as they have not relaxed back to their thermal equilibrium state.                5) Adiabatic polarization compression: This compression can be understood as a set of logical gates (CNOT, SWAP, CSWAP and NOT, to be explained hereinafter) operating on the spins, gates that are practically demonstrated in various labs worldwide. In adiabatic polarization compression polarization is modified such that some spins become more polarized and others become less polarized. Limitation: Shannon's bound (on entropy compression) limits adiabatic polarization compression, and to the best knowledge of the inventors of the present invention no practical application of this method exists.        6) Polarization transfer: If at a given temperature, the spins we want to use (in spectroscopy) are less polarized than other spins, then swapping polarizations with these highly polarized spins is useful, and is equivalent to cooling the spins we want to use. Limitation: The improvement is limited by the spin-polarization of the highly polarized spins. This technique, applied between nuclear spins on the same molecule (and in parallel on all molecules) is common in NMR spectroscopy, but does not provide an impressive polarization increase. Performing polarization swapping between spins on different molecules has the same limitations but opens interesting possibilities, for instance, the use of Xenon recently improved polarization by a factor of 10. Swapping with electrons is much more promising in theory, but is very far from being applicable, because machines that manipulate electron spins cannot be used in NMR spectroscopy. Still if it becomes practical one day, this shall yield an improvement by a factor of up to 1000 of the polarization.        
These latter two techniques developed so far for “effective cooling”, provide some improvement, but the new effective cooling of the present invention appears to be substantially more effective and efficient.
Considering NMR in terms of logic gates we gain a deep insight on the effective cooling processes. If we consider effective cooling in this matter we can use many strong tools of data compression. Both the adiabatic polarization compression and the polarization transfer are then considered as simple logical gates applied onto the spins (that are considered as binary digits, that is, bits). The present invention combines thermalization together with entropy manipulation techniques (adiabatic polarization compression and polarization transfer). Adding thermalization is the contribution of this current invention, because it allows the design of novel cooling techniques, the “algorithmic cooling”, that is not limited by Shannon's bound. Algorithmic cooling can still be fully described via logical gates operating on bits. The main importance of our invention (and a short term application) is to improve signal to noise ratio in NMR, due to improving the polarization bias, that is, cooling some of the spins.
Since we are dealing with spins, which are quantum systems, one needs to use a more complicated language in order to fully describe the implementation in the NMR lab. In order to describe the implementation of algorithmic cooling in the NMR lab, one can use the conventional NMR terminology, but it is more convenient to use the language of quantum gates, which relate to quantum computers. NMR quantum computers are currently the most successful quantum computing devices. The tools developed in NMR quantum computing provide a better insight on how to perform algorithmic cooling in practice.
Furthermore, quantum computing appears to be very important, due to their ability to solve hard problems (and break very important cryptosystems). NMR quantum computers are a special type of quantum computers known as ensemble quantum computers. The widespread belief is that even though ensemble quantum computation is a powerful scheme for demonstrating fundamental quantum phenomena, it is not scalable. Luckily, however, it was shown recently, that the scaling problem does not exist if one uses adiabatic data compression schemes to initialize the quantum computer via polarization compression. Once enough qubits (say, m) are cooled to sufficiently low polarization bias εF, the NMR quantum computer can then be used without any scalability problem. However, as mentioned before, that cooling method is limited due to the Shannon's bound on entropy manipulations.
The second (long-term) use of algorithmic cooling is to allow for scalable NMR quantum computing, which is not limited by Shannon's bound on entropy manipulation.
It is an object of the present invention to present the new cooling technique called algorithmic cooling. Algorithmic cooling combines thermalization with adiabatic data compression, or it combines thermalization with polarization transfer, this variant of algorithmic cooling is called “cooling by thermalization”. The more general algorithmic cooling combines thermalization, polarization transfer, and adiabatic polarization compression. In general we obtain “polarization compression” that is not limited to be adiabatic anymore.
Another object of the present invention is to provide an algorithmic cooling of nuclear spins, which is practical and yields substantial cooling.
Yet another object of the present invention is allowing the application of this method in various NMR techniques (MRI, liquid and solid state NMR) Still another object of the present invention is to provide a most basic algorithmic cooling step that is already applicable to molecules as small as a molecule that contains 3 nuclei with spin ½. In particular, we show that all steps of algorithmic cooling were already implemented on such molecules, some steps on Tri-chloro-ethylene (C2Cl3H) and other steps on Tri-fluoro-bromo-ethylene (C2F3Br).
Another object of the present invention is to present the usefulness of increasing the ratio of thermalization times of different nuclei, for allowing warm spins to cool down while preventing cool spins from warming up. In particular, we show one way of doing that, via the use of the magnetic salt Chromium Acetylacetonate.
Another object of the present invention is to suggest scalable NMR quantum computation initialized by algorithmic cooling as a long-term application.
Other aspects and advantages of the present invention are described hereinafter and will become apparent after reading the present specification and viewing the accompanying figures.